How to remove the "if" part following the calculation result obtained from Solve?

Questions
, ,
1

Solve[ForAll[{x, y},
Equivalent[
m (x/a) + n (y/b) ==
1, ((t1 - t2) (b (-1 + t1 t2) x +
a (b + b t1 t2 - (t1 + t2) y)))/((1 + t1^2) (1 + t2^2)) ==
0]], {m, n}, Reals] // Simplify

2025-10-29_194401.png

The code generates an answer containing “if”. How can I remove the “if” part to obtain the result shown in the bottom image?

2025-10-29_194420.png

2

You can remove the conditions by extracting the first element of the ConditionalExpression:

Solve[ForAll[{x, y}, 
    Equivalent[
     m (x/a) + n (y/b) == 
      1, ((t1 - t2) (b (-1 + t1 t2) x + 
           a (b + b t1 t2 - (t1 + t2) y)))/((1 + t1^2) (1 + t2^2)) == 
      0]], {m, n}, Reals] /. 
  ConditionalExpression -> (#1 &) // Simplify
3

Thanks for your help!

4

Normal[] converts ConditionalExpression[value, condition] to its un-Conditional-ized value:

Normal@Solve[...]